However, under finite populations, evolutionary outcomes are defined not only by whether selection favours or opposes invasion, but also whether it does so with fixation [1]}. In the following sections we will explore some of the possible ways in which fixation probabilities may depend on population size in \(2\times 2\)  games. We found that there were are at least 8 shapes that single mutant fixation probability functions \(\rho _N\)  can take:
